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Simple but very likely true, if people had enough money for essentials from a living wage then they are much less likely to need to borrow small amounts of money at a stupid interest rate to get bread, heat and cider.

Ok - let me try this for a thought experiment. You can impact this problem two ways. You can change peoples incomes by raising the minimum wage or you can change their costs by doing something that reduces the cost of apple based products.

I have enough parliamentary and civil service resource to either cut the price of apple products in half or raise the minimum wage by 25%. Which one is going to lead to the greatest reduction in the use of pay day loans?

Now swap apple based products for cutting rental costs in half though rent controls.

The other point I would raise is there is an underlying assumption that putting up the minimum wage will not affect the level of employment. I would content that may not be true.

Lets take a large grocery chain that has introduced the self service tills that always have an unexpected item in the bagging area. If their staff costs go up by 25% as the minimum wage rises what would they do?

Except of course that most payday loans are used to pay for food, bills and rent rather than commodities. Unless you class a spare bedroom as a commodity.

http://www.theguardian.com/money/2013/oct/01/payday-loans-feed-families-report

Excellent mis-read there fella. I don't think I every suggested people were taking out pay day loans to buy discretionary goods.